Why is the other side faded in mirror mode?
It is by design. The other side will only be available for direct manipulation after you have applied the modifier. Mostly, when a user attach a mirror modifier, it's purpose is so that the user could just focus on working on one side of the model until we need to break the model's symmetry.

The greying out give you a visual as to which side of the model you are currently suppose to work on as you rotate around the model. You can imagine it would be frustrating to be clicking on something that is inactive by design.